Green’s Dictionary of Slang

(US) an important person.

1792		in E. Healey Hist. Alert Bay (1958) 15: The Ty-ee, or chief, of the village paid us an early visit [OED].
1856		in 34th Cong. 3 Sess. H.R. Ex. Doc. 37 75: The chief [...] [seems] to have more real influence than any of the so-called ‘tyhees’ on the Sound [DA].
1877		Puget Sound Argus 23 Nov. n.p.: With the coming of the military among us came a big church ‘tyhee,’ who told us the soldiers were coming to protect us [DA].
1950		R.V. Mills ‘Oregon Speechways’ in AS XXV:2 82: Prolongation of a main vowel intensified meaning; thus tyee meant chief, hyas tyee a big chief, but hya-a-a-s tyee a very great chief or politician [DA].